In a previous post, you advised me that rather than send out new invitations for our rescheduled wedding date, it was more appropriate to send notes or note cards out announcing the new date.
I've done that and am about to send them. (I assume all guests, whether they RSVP'd yes or no, get the new announcement.) But, I already know that a few family members that could not attend on the original date are now able to, and a few that accepted originally now must decline. Should I ask guests to RSVP again, and if so, do I send response cards out, or should I expect them to contact me?
All guests should receive the announcement of the new date for the very reasons you state. You don't need response cards, but include some way of notifying you. Your guest should know how to write a formal response, but we know most don't. As long as they have some way to notify you it is fine.